what is the period of (f(x)=sin(x))?\n(\frac{pi}{2})\n(pi)\n(\frac{3pi}{2})\n(2pi)

Explanation:

Step1: Recall sine - function period formula

The general form of a sine function is $y = A\sin(Bx - C)+D$, and its period $T=\frac{2\pi}{|B|}$.

Step2: Identify B for $y = \sin(x)$

For the function $f(x)=\sin(x)$, we have $A = 1$, $B = 1$, $C = 0$, $D = 0$.

Step3: Calculate the period

Using the formula $T=\frac{2\pi}{|B|}$, substituting $B = 1$ gives $T=\frac{2\pi}{|1|}=2\pi$.

Answer:

D. $2\pi$